In this study, magnetostriction measurements were performed on the ferromagnetic Heusler alloy, Ni2MnGa0.88Cu0.12, which is characterized by the occurrence of the martensitic phase and ferromagnetic transitions at the same temperature. In the austenite and martensite phases, the alloy crystallizes in the L21 and D022-like crystal structure, respectively. As the crystal structure changes at the martensitic transition temperature (TM), a large magnetostriction due to the martensitic and ferromagnetic transitions induced by magnetic fields is expected to occur. First, magnetization (M-H) measurements are performed, and metamagnetic transitions are observed in the magnetic field of μ0H = 4 T at 344 K. This result shows that the phase transition was induced by the magnetic field under a constant temperature. Forced magnetostriction measurements (ΔL/L) are then performed under a constant temperature and atmospheric pressure (P = 0.1 MPa). Magnetostriction up to 1300 ppm is observed around TM. The magnetization results and magnetostriction measurements showed the occurrence of the magnetic-field-induced strain from the paramagnetic austenite phase to the ferromagnetic martensite phase. As a reference sample, we measure the magnetostriction of the Ni2MnGa-type (Ni50Mn30Ga20) alloy, which causes the martensite phase transition at TM = 315 K. The measurement of magnetostriction at room temperature (298 K) showed a magnetostriction of 3300 ppm. The magnetostriction of Ni2MnGa0.88Cu0.12 is observed to be one-third that of Ni50Mn30Ga20 but larger than that of Terfenol-D (800 ppm), which is renowned as the giant magnetostriction alloy.